The norm of the Fourier transform on finite abelian groups

Gilbert, John; Rzeszotnik, Ziemowit

doi:10.5802/aif.2556

The norm of the Fourier transform on finite abelian groups
[La norme de la transformée de Fourier sur les groupes abéliens finis]

Gilbert, John ¹ ; Rzeszotnik, Ziemowit ²

¹ University of Texas Department of Mathematics Austin, TX 78712–1082 (USA)
² Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland)

Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1317-1346.

Résumé
Abstract

Pour les valeurs de $p$ et $q$ comprises entre $1$ et l’infini, nous déterminons la norme de la transformée de Fourier de l’espace $L^{p}$ d’un groupe abélien fini vers l’espace $L^{q}$ du groupe dual.

For $1 \leq p, q \leq \infty$ we calculate the norm of the Fourier transform from the $L^{p}$ space on a finite abelian group to the $L^{q}$ space on the dual group.

EuDML MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2556

Classification : 42C40, 43A15, 43A25
Keywords: Fourier transform, finite abelian groups, wave packets, biunimodular functions
Mot clés : transformée de Fourier, groupes abéliens finis, paquets d’ondes, fonctions bi-unimodulaires

Affiliations des auteurs :

Gilbert, John ¹ ; Rzeszotnik, Ziemowit ²

¹ University of Texas Department of Mathematics Austin, TX 78712–1082 (USA)
² Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland)

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     title = {The norm of the {Fourier} transform on finite abelian groups},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Gilbert, John; Rzeszotnik, Ziemowit. The norm of the Fourier transform on finite abelian groups. Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1317-1346. doi : 10.5802/aif.2556. http://www.numdam.org/articles/10.5802/aif.2556/

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